PSI - Issue 11

Fabio Mazza et al. / Procedia Structural Integrity 11 (2018) 218–225

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Fabio M zza et al. / Structural Integrity Procedia 00 (2018) 000 – 000

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(a)

(b)

Fig. 2. Nonlinear OP modelling of a masonry infill panel: (a) OP five-element model; (b) OP monotonic and hysteretic (pivot) curves.

2.3. In-plane-out-of-plane interaction modelling

As outlined by many experimental studies, the progression of OP masonry damage is notably influenced by previous IP damage. The IP-OP interaction model proposed in the present work is based on the following fundamental hypotheses: i) IP damage produces a reduction of OP values in strength and stiffness; ii) a bilinear hysteretic law is maintained during the OP damage; iii) OP damage is due to occur as soon as IP drift ratio (i.e.  (IP) /h) exceeds the threshold corresponding to the attainment of the maximum IP strength; iv) the effects of OP damage on IP behaviour are not considered. In order to calibrate the relation between maximum values of  (IP) /h and OP decay of strength and stiffness, experimental tests available in the literature are considered with reference to different infill typologies. Firstly, three single-storey single-bay reinforced concrete (r.c.) frame specimens, representing the part of a full-scale r.c. framed structure, are considered, fully infilled with a traditional strong single-leaf unreinforced masonry infill with thickness t w =35 cm (Hak et al. 2014). The OP cyclic tests have been carried out on the specimens previously damaged in-plane, considering three increasing maximum levels of  (IP) /h (i.e. 1.0%, 1.5% and 2.5%). The following expressions for the percentage reduction factor are obtained for the maximum infill OP strength -0.53 69.225 % 42.5 ( OP ) ( OP ) ( IP ) wFAA,damaged wFAA,damaged F ,strong F ,strong ( OP ) ( OP ) wFAA,undamaged wFAA,undamaged F F r [%] , r [ ] F h F             (5a,b) for (  (IP) /h ) less (Eq. 5a) or more (Eq. 5b) than 2.5, and initial infill OP stiffness -1.382 38.369 % 10.8 ( OP ) ( OP ) ( IP ) w1,damaged w1,damaged k ,strong k ,strong ( OP ) ( OP ) w1,undamaged w1,undamaged k k r [%] , r [ ] h k k             (6a,b) using a regression analysis, on the basis that the OP damage starts once the maximum IP strength is reached  i.e.    (IP) /h) lower =0.5%) while residual mechanical properties persist beyond an upper threshold (i.e.    (IP) /h) upper =2.5%) till the OP collapse point. Moreover, the ultimate values of strength and stiffness are evaluated using Eqs. 4a-4c, where  (OP) =0.8 and  (OP) =0.017 are assumed. In a similar way, IP-OP tests on weak infill typology, made with hollow clay brick with horizontal holes and thickness t w =8 cm, have been performed considering three 2/3 scaled single-storey single-bay reinforced concrete (r.c.) frame specimens (Ricci et al. 2017). Preliminary cyclic IP tests were followed by OP monotonic tests, considering: low (0.16%), medium (0.37%) and high (0.58%) levels of  (IP) /h . Expressions for the percentage reduction factor of the maximum infill OP strength -0.9617 17.163 % 21.25 ( OP ) ( OP ) ( IP ) wFAA,damaged wFAA,damaged F ,weak F ,weak ( OP ) ( OP ) wFAA,undamaged wFAA,undamaged F F r [%] , r [ ] h F F             (7a,b) for (  (IP) /h ) less (Eq. 7a) or more (Eq. 7b) than 0.8, and initial infill OP stiffness